This invention relates to well logging methods and apparatus for investigating characteristics of an earth formation traversed by a bore hole and of substances within the bore hole and is based upon physical measurements, such as electrical, acoustical, nuclear or other measurements. The objective of the invention is to express the properties of a substance or of earth formation in terms of an "impulse response function," h(t), which represents the response of the substance or of the earth formation to a burst of energy of a short duration. The energy may be electrical, acoustical, or it may be expressed by a pulse of neutrons or by any radiation pulse. The function h(t) is dependent upon certain significant properties of the substance or of the formation. From the function h(t) one can determine these properties and thus valuable information may be obtained.
In an idealized representation, which may be used in mathematical derivations, an impulse response function h(t) may be approximated by a function known as Green's function. The burst of energy which generates the function h(t) would then be expressed in an idealized form by a "unit impulse" which is a rectangular pulse obtained by keeping the area of the pulse to be equal to unity and allowing the width of the pulse to become infinitisimal, thus causing the height of the pulse to approach infinity. The unit impulse will then be expressed by a function known as the Dirac delta function, .delta.(t), which is specified by the conditions: EQU .delta.(t)=0 for t.noteq.0 (1)
and ##EQU1## where t represents time.
Broadly speaking the impulse response function h(t) describes physical behavior of a material substance or a medium if an "impulse field" were suddenly applied to such a substance or medium. In practical situations the impulse field is represented by an energy burst of a relatively short duration. The impulse field interacts with a substance or a medium and radiations are produced as a result of such interactions.
The intensity of these radiations as they vary with time will then be expressed by the function h(t). The impulse field may be associated with any form of energy or any form of a physical field, such as an electrical field, a radiation field, an acoustic field, a field represented by an assembly or flow of particles which may interact or diffuse through a medium; such as a stream of fast neutrons or photons, a cloud of thermal neutrons, etc. The impulse response function h(t) may be defined as "associated" with:
(1) a particular type of the field (or with a particular type of radiant energy represented by the field) and with
(2) a particular response of a material medium or of a substance interacting with the field or with a particular radiation which represents this response.
As an example, it can be said that the impulse response function h(t) is "associated" with neutrons representing an applied field, and at the same time it may be associated with gamma rays representing the response of a medium to the applied field. The neutrons may have a specified energy or a specified energy spectrum. To be specific, an impulse response function, h(t), may be associated with 14 MeV neutrons and gamma rays having energies from 3.43 MeV to 10 Mev.
Many efforts have been made in the past to develop successfully methods and apparatus for obtaining impulse response functions of formations traversed by a bore hole. These methods and apparatus of the prior art were applied mainly to nuclear and acoustical well logging. Procedures used in nuclear logging were described, for instance, in the U.S. Pat. No. 3,379,882 issued to A. H. Youmans on Apr. 23, 1968; in the U.S. Pat. No. 3,509,346 issued to W. R. Mills, Jr., et al. on Apr. 28, 1970; in the U.S. Pat. No. 3,662,179 issued to A. H. Frentrop et al. on May 9, 1972 and in numerous other patents. It has been customary in the prior art to irradiate formations with discrete bursts of high energy neutrons usually obtained by means of generators of the deuterium-tritium type. Each burst produced in the formations traversed by a bore hole and within the fluid in the bore hole a population or a cloud of thermal neutrons which rapidly increased, attained a maximum and then slowly decayed with time. Radiation detectors were used for directly measuring the intensity of such a cloud, during an appropriate time interval following a neutron burst. The function which described the variation in intensity of a cloud was termed "neutron decay function." The term "impulse response function" introduced in this specification has a meaning which is broader than that of the "neutron decay function" and it is used in nuclear well logging as well as in other forms of well logging.
In the measurements of the prior art, the time intervals separating successive neutron bursts had to be relatively large so as to allow the neutron decay function to die out before the succeeding neutron burst began. The disadvantages of this technique were principally in their low efficiency, as the pulsed neutron source was utilized during a relatively small fraction of time. In well logging used for oil exploration, each burst of fast neutrons lasted typically 30 microseconds and the time intervals separating the bursts were approximately 2000 microseconds. Thus the pulses were produced at a repetition rate of 500 pulses per second. Consequently, the utilization factor of the source was of the order of 1.5%.
A very low utilization factor of the radiation source was also encountered in uranium exploration and, particularly in uranium exploration by means of delayed fission logging as disclosed in the U.S. Pat. No. 3,686,503 issued to W. W. Givens et al. on Aug. 22, 1972. It is well known by those skilled in the art, that earth formations may be characterized with regard to their uranium content on the basis of delayed neutrons resulting from neutron fission of uranium. When a formation containing a uranium ore is irradiated with neutrons, the uranium nuclei react to neutron bombardment by breaking into smaller nuclear fractions which are normally referred to as fission products. The fission of uranium is attended by the emission of prompt neutrons immediately upon occurrence of the fission reaction and also by the emission of delayed neutrons subsequent to the fission process. The delayed neutrons are emitted by the fission products for an appreciable length of time following the fission reaction and the most abundant delayed neutron group exhibits the half life of about 2.3 seconds. Givens et al. pointed out, in the aforementioned U.S. Pat. No. 3,686,503 that the source of fast neutrons should be operated, approximately, at two bursts per second, each burst having a duration of about three microseconds. Consequently, the utilization factor of the neutron source was only 0.0015%.
Numerous efforts have also been made to obtain impulse response functions in acoustical logging as suggested in the U.S. Pat. No. 3,962,674 issued to E. P. Howell on June 8, 1976 and in other patents. It was customary in acoustical logging to employ a downhole sonde which contained a generator of acoustic energy pulses and a detector for receiving pulses from the environment adjacent to the sonde. The generator transmitted, repetitively, at relatively large intervals of time, short acoustic energy bursts to the environment adjacent to the sonde. The detector received several acoustic pulses produced by each burst and a recorder connected to the detector made a record of the arrivals and shapes of the detected pulses. Such a record was a record of an "impulse response function" defined in this specification. When an acoustic energy burst is transmitted from the sonde to the surrounding environment it follows a number of paths of differing nature in order to get to the detector. Some of these paths are through the casing, and cement behind the casing. Others are through solid particles of sand and rock. Others are through solids and partially through interstitial fluids or through the interconnected fluid-filled pore spaces alone. Knowing the impulse response function, various individual pulses produced by each burst may be identified. Knowing the distance between the generator and the detector, the velocities of these pulses and, consequently, the properties of the formations, may be determined by measuring the time of travel between the generator and the detector. It was necessary in the procedures of the prior art to have the time intervals between the acoustic energy bursts produced by the generator to be relatively large. Each succeeding burst should have been produced after a time interval that has allowed all individual pulses produced by a burst to arrive at the detector. The disadvantages were similar to those encountered in nuclear well logging. The generator was utilized at a relatively small fraction of time.
E. B. Blankov and Iu. V. Kormiltsev have recently described in the USSR Pat. No. 407,260, issued on Nov. 21, 1973, a different method for obtaining an impulse response function in nuclear well logging. This method was based on correlations. According to the disclosure in that patent, the impulse response function h(t) was obtained by cross-correlating fluctuations in the output of an isotopic neutron source, such as a Po-Be source with fluctuations in the output of a radiation detector placed at an appropriate distance from the source. The disadvantage of this method was in its low efficiency. Because of a relatively low intensity of commercially available isotopic neutron sources, it would have required a long time to perform a crosscorrelation measurement at each depth of the bore hole. This by itself would make it difficult to apply the method in commercial operations.
Measurements of neutron decay times in the prior art were based on an assumption that the population of thermal neutrons in the fluid within the bore hole dies away substantially faster than in the formations surrounding the bore hole. It was well understood by those skilled in the art that, generally, measurements representing the formations were more desirable than those which represented the fluid. Accordingly, the decay constant associated with the slower decay time (or slower neutron lifetime) was measured. A record was made of the impulse response function of the type EQU h(t)=Me.sup.-.gamma.t ( 3)
where M and .gamma. are constants. The decay constant .gamma. can be expressed as .gamma.=v.SIGMA. where v=2.2.multidot.10.sup.5 cm/sec is the velocity of thermal neutrons and .SIGMA. is the macroscopic cross section for capture of thermal neutrons of the medium in which the slowing down process occurred. The quantity .SIGMA. was interpreted as representing the macroscopic cross section for capture of thermal neutrons in the formations surrounding the bore hole.
However, the expression of the equation (3) did not always give sufficiently useful information. The information was useful when drilling fluids in the bore hole, having high chlorine content (and correspondingly fast decay time) were encountered. However, the information was not sufficiently useful when the bore hole contained air, gas, fresh water or oil. In such cases, the procedures of the prior art could not have been used.
In nuclear well logging as in other nuclear measurement techniques the problems dealing with the background noise were encountered and efforts were made to improve the signal to noise ratio in these measurements. These efforts were not entirely successful.